Jen had 35 as many stamps as Kathy. The sum of the number of stamps Jen and Kathy had was the same as the number of stamps that Betty had. After trading, Betty gave 10% of her stamps to Jen and received 40% of Kathy's stamps. After that, Kathy continued to trade and increased her number of stamps in the end by 20%, find the ratio of her number of stamps to the sum of Jen's and Betty's stamps in the end.
| |
Jen |
Betty |
Kathy |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
3.8 u |
9.2 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
12.4 u |
3.6 u |
16 u |
Total number of stamps that Jen and Kathy had at first
= 3 u + 5 u
= 8 u
Number of stamps that Betty had at first = 8 u
Number of stamps that Betty gave to Jen
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of stamps that Betty received from Kathy
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of stamps that Kathy increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of stamps that Jen and Betty had in the end
= 3.8 u + 9.2 u - 0.6 u
= 12.4 u
In the end
Kathy : Jen and Betty
3.6 : 12.4
360 : 1240
9 : 31
Answer(s): 9 : 31
